Testing Predictor Significance Across Overlapping Returns

Summary

The document asks how to test whether a proposed predictor forecasts weekly stock market returns when observations are formed from overlapping daily windows. Because adjacent weekly returns share days, their errors may be correlated, so a test designed for a single independent return may give an unreliable variance estimate. The question seeks an appropriate null hypothesis test and test statistic that accounts for this dependence.

No answer, derivation, empirical result, or citation is provided. The document therefore identifies an inference problem rather than prescribing a solution. Any application would need to specify the predictive regression and use an inference method suited to serially correlated errors; the source itself does not establish which estimator or procedure is correct.

Key ideas

• Overlapping return windows can induce correlation between forecast errors.
• A single-return variance calculation may not be appropriate for testing predictability across multiple returns.
• The document raises, but does not answer, the question of which test statistic and variance estimator to use.

Tags

# Testing predictability of a proposed predictor in case of multiple returns


# Testing predictability of a proposed predictor in case of multiple returns












Say I have a T daily observations for the last ten years on a new predictor $x_t$ which I think is a predictor of the expected weekly return on the stock market, $r_{t,t+5} = r_{t+1}+...+r_{t+5}$, where $r_t$ is log return for that period. In this case, how can I test the null hypothesis that $x_t$ has no predictability? The answer would be simple if we are concerned about only one return. But, here, I want to test the predictability for multiple returns which may be correlated with each other. Any idea how to test the hypothesis correctly? What's the correct test statistic and variance of it? Reference to a procedure or an academic paper is also welcome!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.